Question

Let the function f be defined by f(x)=\(\frac{9+3x}{7-2x}\), then f^-1(x) is ______

(a) \(\frac{9-3x}{7+2x}\)

(b) \(\frac{7x-9}{2x+3}\)

(c) \(\frac{2x-7}{3x+9}\)

(d) \(\frac{2x-3}{7x+9}\)

This question was addressed to me during an online interview.

This key question is from Composition of Functions and Invertible Function in section Relations and Functions of Mathematics – Class 12

Answer 1

Right answer is (b) \(\frac{7x-9}{2x+3}\)

To explain I would say: The function f(x)=\(\frac{9+3x}{7-2x}\) is bijective.

∴ f(x)=\(\frac{9+3x}{7-2x}\)

i.e.y=\(\frac{9+3x}{7-2x}\)

7y-2xy=9+3x

7y-9=x(2y+3)

x=\(\frac{7y-9}{2y+3}\)

⇒f^-1 (x)=\(\frac{7y-9}{2x+3}\).